Given a sequence of nonnegative real numbers λ0, λ1… which sum to 1, we consider random graphs having approximately λi n vertices of degree i. Essentially, we show that if Σ i(i - 2)λi > 0, then such… Expand

The term Probabilistic Method refers to the proof of deterministic statements using probabilistic tools. The method has been successfully applied to a number of problems in the field of graph… Expand

We show that if ∑i(i−2)λi<0 then the graph a.s. has a giant component, and that the structure of the graph remaining after deleting C is basically that of a random graph with n′=n−∣C∣ vertices.Expand

Consider a randomly generated boolean formula F (in the conjunctive normal form) with m clauses of size k over n variables; k is fixed at any value greater than 1, but n tends to infinity and m = (1 + o(1))cn for some c depending only on k.Expand

We present an O(mn) algorithm to determine whether a graph G with m edges and n vertices has an odd cycle transversal of order at most k, for any fixed k.Expand

We show that for any fixed <italic>k</italic>, there is a linear-time algorithm which gives an approximate separator algorithm for determining if a graph has a tree decomposition of width at most k.Expand